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Full text of "Text Book Of Mechanical Engineering"

Moment of Inertia, and Stress Area.

431

To find the Moment of Inertia of any Beam Section.

-Proceed as in the last construction and find Z.
nd I = Zjy.*    So for rectangular sections
bJP     h    ^bh*

62      12

Then Z = -

y

.

\   —
X   ---

Stress areas for circle, hollow circle, triangle, and hollow
•ectangle we shewn in Fig. 385, being measured as in Fig. 372
mean width x - Y The centre of gravity of each area is obtained
y cutting out in stiff paper and hanging up in two different

,|tf_   -    .....O —— —- —y

>ositions to mark two plumb lines, which will cross at G. For
he triangular beam the neutral axis must be drawn at ^ the
leight, a line of limiting stress drawn across the apex, and another
>elow, at an equal distance from its axis. Projecting and con-
urging, we shall obtain the areas shewn, which must be equal.
The results are as follows :
Moment of resistance of circle                =f'og82 d*

of hollow circle      =7-0982 :

D

of triangle

=7-0417

of hollow rectangle =7'1666:

H

* See also note, page 430; see also page 845.